I feel like when it comes to polyamourous relationship there are only 3 people involved. Is the case or is that just the most common situation?
That is not the case - it may just be that you have mostly encountered 3-person poly arrangements, but that doesn’t mean polyamory is limited to 3 people. Someone who is poly may be only dating one other person, but that relationship can still be considered polyamorous - I currently have two partners; but if I broke up with one, my relationship with my other partner wouldn’t suddenly become monogamous.
If someone is dating two other people, and if each of those people are also dating one other person, then five people are involved. If four people are in a closed relationship, all dating each other but no one else, then four people are involved. And so on.
It also depends on how you define “involved” - at one point, my poly network included at least a dozen people and probably more, if you tracked all the connections. Say I’m dating three people: each of those individual relationships only “involves” two people; but my personal poly situation “involves” four people (including myself). And if my partners are dating other people, and those other people are also dating other people, the number quickly grows! I might not have direct relationships with everyone, but they are still “involved” in the sense that if abuse, an STI, or any kind of drama impacts one of them, it also impacts me and the health of my relationships.
It is important to remember that every social network and every cultural bubble has its own norms! You may simply know a bunch of poly people who tend towards three-person closed triads; but someone else might be in a world where it’s far more normal for lots of individuals to have lots of cross-networked relationships (as was the case at my college). Always know and own your truth, but never assume that your truth is the truth!